level 8 questions - emaths
TRANSCRIPT
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 1
Mental Questions
1. What number is five cubed?
2. A circle has radius r. What is the formula for the area of
the circle?
3. Jenny and Mark share some money in
the ratio two to three. Jenny’s share is
one hundred and ten pounds.
How much is Mark’s share?
4. The net of a triangular prism is made from triangles and rectangles.
How many of each shape are needed?
5. Multiply minus six by minus two.
Births
The table shows data about births in the UK.
Year Number of births
1910 1.05 × 106
1920 1.13 × 106
1930 7.69 × 105
1940 7.02 × 105
1950 8.18 × 105
1960 9.18 × 105
1970 9.04 × 105
1980 7.54 × 105
1990 7.99 × 105
(a) In which year was the number of births the highest?
...............................
1 mark
(b) How many more births were there in 1990 than in 1980?
Show your working and write your answer in standard form.
...............................
2 marks
Trigonometry
(a) Calculate the value of y
Show your working.
37º
14 y
Not drawnaccurately
y = ................... 2 marks
12 cm15 cm
Calculations:
Decision: Yes No
50º
2 marks
Is it possible to have a triangle with the angles and lengths shown below?
For each triangle, show calculations then tick () Yes or No.
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 2
Mental Questions
1. What is one third of three-quarters of
one hundred?
2. I’m thinking of a number. I call it n. I square my number then add four.
Write an expression to show the result.
3. Twenty-one out of thirty-six pupils said they watched Top of the Pops.
What angle would show this on a pie
chart?
4. There are seven red and three blue balls in a bag.
I am going to take a ball out of the bag
at random. What is the probability
that the ball will be blue?
5. Write a multiple of three that is
bigger than one hundred.
Enlargement Here are four pictures, A, B, C and D. They are not to scale.
A
C
B
D
5.6 cm 5.6 cm
h cm h cm
4 cm
4 cm
6 cm
6 cm
(a) Picture A can be stretched horizontally to make picture B. Show that the horizontal factor of enlargement is 1.5
1 mark
(b) Picture A can be stretched vertically to make picture C. The vertical factor of enlargement is 1.25
What is the height, h, of picture C?
............................. cm
1 mark (c) Show that pictures A and D are not
mathematically similar.
1 mark
(d) Picture E (not shown) is mathematically similar to picture A. The width of picture E is 3 cm
What is the height of picture E?
Factors
(a) Look at these equations.
48 = 3 × 2a 56 = 7 × 2b
What are the values of a and b?
a = ............................... b = ...............................
1 mark
(b) 48 × 56 = 3 × 7 × 2c
What is the value of c?
c = ............................... 1 mark
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 3
Mental Questions
1. I am thinking of a number. I call it n. I double my number then I subtract three.
Write an expression to show the result.
2. What percentage of fifty pounds is thirty-
five pounds?
3. On average, the driest place on earth gets
only nought point five millimetres of rain every
year.
In total, how much rain would it expect to get
in twenty years?
4. To the nearest whole number, what is the
square root of eighty-three point nine?
5. It takes me one and a half minutes to swim
one length of the pool.
How many lengths can I swim in fifteen
minutes
Box plots
A pupil recorded the heights of all the girls in year 7. She summarised her results, then drew this box plot.
136 140 144 148 152 156 160
Height (cm)
shortestlower
quartile medianupper
quartile tallest
Year 7 girls
The pupil compared the heights of year 7 boys with year
7 girls.
• the shortest boy was the same height as the shortest girl;
• the range of boys’ heights was greater than the range of girls’ heights;
• the inter-quartile range of boys’ heights was smaller than the inter-quartile range of girls’ heights.
(a) Draw what the box plot for boys could look like.
136 140 144 148 152 156 160
Height (cm)
Year 7 boys
2 marks
There are 120 girls in year 9
The cumulative frequency diagram shows information about their heights.
120
100
80
60
40
20
0
Height (cm)
Cumulativefrequency
130 135 140 145 150 155 160 165 170 175
(b) Compare the heights of year 9 girls with year 7 girls.
3 marks
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 4
Mental Questions
1. Tariq won one hundred pounds in a maths
competition. He gave two-fifths of his prize
money to charity. How much of his prize
money, in pounds, did he have left?
2. What is three point nine divided by two?
3. The instructions for a fruit drink say to mix one part blackcurrant juice with four parts
water. I want to make one litre of this fruit
drink. How much blackcurrant juice should I
use? Give your answer in millilitres.
4. What is half of two-thirds?
5. The population of the United Kingdom is about fifty-nine million. Write this number in
figures.
A cup of coffee costs £1.75 The diagram shows how much money different people get when you buy a cup of coffee.
Retailers get 44p
Growers get 5p
Others get £1.26Cup of coffeecosts £1.75
Not drawnaccurately
(a) Complete the table to show what percentage of the cost of a cup of coffee goes to retailers, growers and others.
Show your working.
Retailers %
Growers %
Others %
2 marks
(b) Some people think the growers should get more. Suppose the percentages change to:
Retailers 23%
Growers 10%
Others 67%
Suppose the retailers still got 44p from each cup of coffee sold. How much would a cup of coffee cost? Show your working.
£
2 marks
Graphs
Match each graph to the correct equation.
ED yy
xx
A y
x
B y
x
C y
x
Graph ………… shows the equation y = 2x – 6
Graph ………… shows the equation y = 6x3
Graph ………… shows the equation y = 6 – x
Graph ………… shows the equation y = x2 – 6
Graph ………… shows the equation y =
x61
2 marks
Tiles
A pupil has three tiles.
One is a regular octagon, one is a regular hexagon, and one is a square.
The side length of each tile is the same.
The pupil says the hexagon will fit exactly like this.
Not drawn accurately
Show calculations to prove that the pupil is wrong.
3 marks
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 5
Mental Questions
1. What is three-fifths of forty pounds?
2. The longest bone in the human body is in the leg. The average length of this bone in a man is fifty
centimetres. In a woman it is ten per cent less.
What is the average length of this bone in a
woman?
3. Using three as an approximation for pi, what is the area of a circle with radius five centimetres?
4. I am thinking of a two-digit number that is a multiple of eight.
The digits add up to six.
What number am I thinking of?
5. I am thinking of a number. I call it n. I add five to my number.
Write an expression to show the result.
Plant Pots
These plant pots are mathematically similar. The internal dimensions are shown.
NOT TOSCALEm cm
40cm
42cm
60cm
(a) Calculate the value of m.
Show your working.
m = ……………… cm
2 marks (b) The capacity, C, of a plant pot in cubic
centimetres is given by the formula:
C= 121 πh (a2 + ab + b2)
h cm
a cm
b cm
In the larger plant pot a = 60, b = 36 and h = 42 How many litres of compost are needed to fill the plant pot?
Show your working.
……………… litres
3 marks
(c) Think about the ratio of the widths of the two plant pots.
Explain why the ratio of the capacity of the smaller pot to the capacity of the larger pot is 8 : 27
1 mark
Languages
100 students were asked whether they studied French or German.
39 27 30
4
French German
27 students studied both French and German.
(a) What is the probability that a student chosen at random will study only one of the languages?
1 mark
(b) What is the probability that a student who is studying German is also studying French?
1 mark (c) Two of the 100 students are chosen at random.
Circle the calculation which shows the probability that both the students study French and German?
10027
10027
9926
10027
10026
10027 ×××
10027
10027
10026
10027 ××
1 mark
Scores
(a) A fair coin is thrown. When it lands it shows heads or tails.
Game: Throw the coin three times.
Player A wins one point each time the coin shows a head. Player B wins one point each time the coin shows a tail.
Show that the probability that player A scores three
points is 8
1
1 mark
(b) What is the probability that player B scores exactly two points?
Show your working.
2 marks
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 6
Mental Questions
1. Five percent of a number is 8. What is the
number?
2. A fair spinner has eight equal sections with a number on each section. Five of them are even
numbers. Three are odd numbers.
What is the probability that I spin an even
number?
3. I can make a three-digit number from the digits two, three and four in six different ways.
How many of these three-digit numbers are
even?
4. What is the volume of a cuboid measuring five
centimetres by six centimetres by seven
centimetres?
5. What is the remainder when you divide three
hundred by twenty-nine?
Theme Park Tom did a survey of the age distribution of people at a theme
park.
He asked 160 people.
The cumulative frequency graph shows his results.
160
140
120
100
80
60
40
20
0
Cumulativefrequency
0 10 20 30 40 50 60 70 80Age (years)
(a) Use the graph to estimate the median age of people at the theme park.
median = ...............................years
1 mark
(b) Use the graph to estimate the interquartile range of the age of people at the theme park.
Show your method on the graph.
interquartile range = ...................................years
2 marks
(c) Tom did a similar survey at a flower show.
Results: The median age was 47 years. The interquartile range was 29 years. Compare the age distribution of the people at the flower show with that of the people at the theme park.
1 mark
Eating
People were asked if they were considering changing what they eat.
29% of the people asked said yes.
Of these, 23% said they were considering becoming vegetarian.
What percentage of the people asked said they were considering becoming vegetarian?
…………………… %
1 mark
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 7
Mental Questions
1. Twenty-five per cent of a number is seven.
What is the number?
2. There are fourteen girls and thirteen boys in a class.
What is the probability that a pupil chosen at
random will be a girl?
3. The first even number is two. What is the hundredth even number?
4. The mean of two numbers is 8. One of the numbers is two. What is the other number?
5. How many edges are there on a square based pyramid?
Tanks
On a farm many years ago the water tanks were filled using a bucket from a well.
(a) The table shows the numbers of buckets, of different capacities, needed to fill a tank of capacity 2400 pints.
Complete the table:
Capacity ofbucket (pints)
Number ofbuckets
8
200
10 12 15 16
150 100 80
(b) Write an equation using symbols to connect T, the capacity of the tank, B, the capacity of a bucket, and N, the number of buckets.
1 mark (c) Now tanks are filled through a hosepipe connected to a
tap. The rate of flow through the hosepipe can be varied.
The tank of capacity 4000 litres fills at a rate of 12.5 litres per minute. How long in hours and minutes does it take to fill the tank?
Show your working.
............... hours ............... minutes
2 marks
(d) Another tank took 5 hours to fill at a different rate of flow. How long would it have taken to fill this tank if this rate of flow had been increased by 100%?
............... hours ............... minutes 1 mark
(e) How long would it have taken to fill this tank if the rate of low had been increased by only 50%?
Show your working.
............... hours ............... minutes 2 marks
(f) This tank, measuring a by b by c, takes 1 hour 15 minutes to fill.
b
ca
How long does it take to fill 2a by 2b by 2c, at the same rate of flow?
2a2b
2c
Show your working.
2 marks
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 8
Mental Questions
1. Multiply 8.7 by 2
2. A bat flies at an average speed of 32 kilometres an hour. At this speed, how far will it fly in 15
minutes?
3. Multiply the brackets (2x +1) (x – 1)
4. I’m thinking of a number. I call it t. I half it and subtract five. Write an expression to show the
result.
5. The first odd number is 1. What is the
hundredth odd number?
Squares
Some numbers are smaller than their squares.
For example: 7 < 72
(a) Which numbers are equal to their squares?
2 marks
(b) Some numbers are bigger than their squares.
Describe this set of numbers.
2 marks Expressions
(a) This solid is a prism, with height 3x. The cross-section is shaded.
x2x
2x
3x
4x
Write an expression for the volume of the solid.
Show your working and simplify your expression.
2 marks
The volume of this prism is given by the expression 8x3 sin a
2x
x4x
a
NOT TO SCALE
(b) What value of a would make the volume of the
prism 8x3?
1 mark
a = .............………...°
(c) The prism has a volume of 500cm3. The value of a is 30°
What is the value of x?
Show your working.
x = ...........……....... cm
2 marks
Not to scale
Algebraic expressions
Look at these expressions.
5 – 8y 3 + 5y
firstexpression
secondexpression
(a) What value y of makes the two expressions equal?
Show your working.
y = …………………
2 marks
(b) What value of y makes the first expression twice as great as the second expression?
Show your working.
y = …………………
2 marks
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 9
Mental Arithmetic Questions
1. Add four to minus five.
2. What number should you add to minus
three to get the answer five?
3. How many nought point fives are there in ten?
4. On average, the driest place on earth gets only nought point five millimetres of rain
every year. In total, how much rain would
it expect to get in twenty years?
5. What is the sum of the angles in a
rhombus?
Which is Bigger?
The diagram shows parts of two circles, sector A and sector B
radius 5cm radius 4cm
A B
of a circle of a circle18
15
(a) Which sector has the bigger area?
Show working to explain your answer.
2 marks
(b) The perimeter of a sector is made from two straight lines and an arc.
Which sector has the bigger perimeter?
Show working to explain your answer.
2 marks
(c) A semi-circle, of radius 4cm, has the same area as a complete circle of radius r cm
4cm
r cm
What is the radius of the complete circle?
Show your working
r = ………………… cm
2 marks
KS3 MATHEMATICS
10 4 10
Level 8 Questions
Day 10
Mental Questions
1. It takes some-one one and a half minutes to swim the length of the pool. How many
lengths can I swim in 15 minutes?
2. Multiply minus eight by minus three.
3. If 4x + 3 = 23, what is the value of x?
4. I have a fair eight sided dice numbered 12
to 19. What is the probability that I will
throw a prime number?
5. What must I multiply n squared by to get
n cubed?
Thomas the Tank Engine
The first ‘Thomas the Tank Engine’ stories were written in 1945.
In the 1980s, the stories were rewritten. The cumulative frequency graph shows the numbers of words
per sentence for one of the stories.
70
60
50
40
30
20
10
00 10 20 30
Number of words per sentence
Cumulativefrequency
Key
Oldversion
Newversion
There are 58 sentences in the old version.
There are 68 sentences in the new version.
3 marks
(a) Estimate the median number of words per sentence in the old version and in the new version.
Show your method on the graph.
old ………...…………
new ……….………… 3 marks
(b) What can you tell from the data about the number of words per sentence in the old version and in the new version?
1 mark
(c) Estimate the percentage of sentences in the old version that had more than 12 words per sentence.
Show your working.
………………… % 2 marks